Q152 / 160 · TS EAMCET 2024 (09 May Shift 2) · Physics

The natural frequency of an LC circuit is 120 kHz . When the capacitor in the circuit is totally filled with a dielectric material, the natural frequency of the circuit decreases by 20 kHz . Dielectric constant of the material is

  • A
    3.33
  • Correct answer
    B
    1.44
  • C
    2.12
  • D
    1.91

Solution

Given Natural frequency of LC Circuit, $f=120 \mathrm{kHz}$ Frequency of $L C$ circuit, $f=\frac{1}{2 \pi \sqrt{L C}}$ On introducing dielectric of dielectric constant K frequency, $\mathrm{f}^{\prime}=\frac{1}{2 \pi \sqrt{\mathrm{~L}(\mathrm{KC})}}=100 \mathrm{kHz}$ $\begin{aligned} & \frac{\mathrm{f}}{\mathrm{f}^{\prime}}=\frac{1}{\sqrt{\mathrm{LC}}} \times \frac{\sqrt{\mathrm{KLC}}}{1}=\sqrt{\mathrm{K}} \\ & \Rightarrow \frac{120}{100}=\sqrt{\mathrm{K}} \Rightarrow \mathrm{~K}=1.44 \end{aligned}$

Hence, the correct answer is option: 'B'.

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